• Cyberian's Gold

    Which of the following reason(s) lead towards the numerical integration methods?

    547f37ca-8a83-45fc-8aea-643d49e70b66-image.png

  • Cyberian's Gold

    In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

    cffe2be2-8461-4d19-87ad-9c649cf71d19-image.png

  • Cyberian's Gold

    Given that dydt=t+y√ with the initial condition y0=1att0=0 find the 3rd term in Taylor series when t=1, y/ =0.2, y// =2, and h=0.1.

    a79db95d-f6c7-46ab-935d-94b79ca2934b-image.png

  • Cyberian's Gold

    Given that dydt=y−ty+t with the initial condition y=1,t=0 Using Euler’s method, y at
    h=0.01
    ; the value of y(0.01)is

    57cdb750-fe84-4d7f-80dc-9a57de5f80d8-image.png

  • Cyberian's Gold

    Given that dydt=1−y√ with the initial condition y0=1att0=0 find the 3rd term of Taylor series when t=0.5 and y// =0.25.

    dc430dd9-c881-4a67-a1a2-447bfa85941c-image.png

  • Cyberian's Gold

    While employing Trapezoidal and Simpson Rules to evaluate the double integral numerically, by using Trapezoidal and Simpson rule with respect to -------- variable/variables at time

    Single
    Both

  • Cyberian's Gold

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    At which of the following points the Maximum value of 2nd derivative of function
    f(x) = -(2/x) in the interval:[1,4] exits?

    d6f1aa7e-ac71-4d6f-9090-9a5178926596-image.png

    At x=1

  • Cyberian's Gold

    At which of the following points the Maximum value of 2nd derivative of function
    f(x) = -(2/x) in the interval:[1,4] exits?

    d6f1aa7e-ac71-4d6f-9090-9a5178926596-image.png

  • Cyberian's Gold

    Given that dydt=t+y√ with the initial condition y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

    86f14116-9455-410f-a4ab-3d9891d5ebaa-image.png

  • Cyberian's Gold

    In Trapezoidal rule, we assume that f(x) is continuous on [a, b] and we divide [a, b] into n subintervals of equal length using the ………points.

    n
    n+1
    n-1
    None of the given choices

  • Cyberian's Gold

  • Cyberian's Gold

    In Simpson’s rule, we can estimate the integral by …………the areas under the parabolic arcs through three successive points.
    Adding
    Subtracting
    Multiplying
    None of the given choices

  • Cyberian's Gold

    Trapezoidal rule of integration of a definite integral is of…………

    O(h2)
    O(h3)
    O(h4)
    None of the given choices

  • Cyberian's Gold

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

    Rectangular method
    Trapezoidal method
    Simpson’s 1/3 Rule
    Simpson’s 3/8 Rule
    241b49e0-041a-44d8-8b26-50765c487568-image.png

    Trapezoidal method

  • Cyberian's Gold

    Which of the following method is simplest one to integrate numerically a given tabular function but give more error?

    Rectangular method
    Trapezoidal method
    Simpson’s 1/3 Rule
    Simpson’s 3/8 Rule
    241b49e0-041a-44d8-8b26-50765c487568-image.png

  • Cyberian's Gold

    Given that dy/dt=t+y with the initial condition y0=1at t0=0 find the 3rd term in Taylor series when t=1.5 and y// =0.6

    db899af0-5e95-40ca-aa5f-c2aa0eef7e0a-image.png

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